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We investigate bond percolation on the non-planar Hanoi network (HN-NP),which was studied in [Boettcher et al. Phys. Rev. E 80 (2009) 041115]. Wecalculate the fractal exponent of a subgraph of the HN-NP, which gives a lowerbound for the fractal exponent of the original graph. This lower bound leads tothe conclusion that the original system does not have a non-percolating phase,where only finite size clusters exist, for p>0, or equivalently, that thesystem exhibits either the critical phase, where infinitely many infiniteclusters exist, or the percolating phase, where a unique giant componentexists. Monte Carlo simulations support our conjecture.

Absence of the non-percolating phase for percolation on the non-planar Hanoi network